Order-type Henstock and McShane integrals in Banach lattice setting

TL;DR

This paper investigates Henstock-type integrals for functions valued in Banach lattices, focusing on their properties in a compact metric space with a regular measure, including the unit interval.

Contribution

It extends the theory of Henstock and McShane integrals to functions in Banach lattices within a metric measure space setting.

Findings

Analysis of Henstock-type integrals in Banach lattices

Extension of integrals to functions on compact metric spaces

Application to the unit interval with Lebesgue measure

Abstract

We study Henstock-type integrals for functions defined in a compact metric space $T$ endowed with a regular $\sigma$-additive measure $\mu$, and taking values in a Banach lattice $X$. In particular, the space $[0,1]$ with the usual Lebesgue measure is considered.